Metatron’s Cube

The Platonic Solids · a map

Start with one circle. By the end there will be thirteen, seventy-eight lines, and — so the claim goes — every perfect solid. Watch it drawn, and check the claim.

Draw · 1

One circle

Everything here is made with a compass and a straight edge. One circle, any size. Its centre is the only point you are given.

Draw · 2

The Seed of Life

Set the compass on the edge of the first circle and draw again. Keep stepping round. Six fit exactly — a radius walks round its own circle six times.

Draw · 3

The Fruit of Life

Carry the pattern outward and thirteen circles stand out that only touch — none overlapping. These thirteen centres are all the figure needs.

Draw · 4

Every line

Join each centre to every other. Thirteen points make seventy-eight lines. That is Metatron’s Cube — the name is modern; the kind of drawing is old.

Find · 1 of 5

Tetrahedron

four triangles · fire

The sharpest and lightest. Plato gave it to fire — the one that cuts. It is here, exactly.

Find · 2 of 5

Cube

six squares · earth

The steadiest thing to stand on; Plato gave it earth. Here, exactly — the hexagon is a cube seen corner-on.

Find · 3 of 5

Octahedron

eight triangles · air

Balanced on a point, turning easily. Air. Here, exactly — two triangles, one in front, one behind.

Find · 4 of 5

Icosahedron

twenty triangles · water

Nearly round, rolling like water. Close — not exact. Its true corners sit at the golden ratio, and a grid of equal circles cannot make that number. The eye forgives it.

Find · 5 of 5

Dodecahedron

twelve pentagons · the whole heaven

The one Plato kept apart, for the cosmos itself. It isn’t here. Every drawing that shows it adds lines the thirteen points don’t give. Look — you won’t find a pentagon anywhere.

Three are really there. Two you have to bring yourself.

Plato, Timaeus, for the elements. The geometry is checkable with a compass; so is the claim.

scroll to draw

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